The justices have been silent on a petition filed by the president's attorneys in October seeking to reverse lower court rulings that would force his longtime accounting firm to hand over his financial information to New York investigators examining potential tax and insurance fraud.
With no firm deadline for the court to act, and no indication of when it may do so, it is becoming increasingly likely that Trump could leave office with the case unresolved.
It is not immediately clear whether the president benefits from the justices' inaction. While Trump's exit could weaken some of his legal arguments, investigators have warned that delays are hamstringing their efforts.
It has been more than a year since Manhattan District Attorney Cy Vance Jr. obtained a subpoena for the high-profile records, which include returns for the president and his businesses dating to 2011.
In his legal arguments, Trump has asserted that the subpoena for his records is particularly burdensome because of the demands of his job as president.
That argument will fade away when he returns to life as a private citizen. On the other hand, it's possible some of the potential crimes Vance is investigating carry statutes of limitations in danger of running out.
Nearly six months have passed since Trump lost his first attempt to keep the records private at the Supreme Court. The court ruled 7-2 against the president, and sent the case back to the lower courts.
In the time since, Trump lost an election to President-elect Joe Biden, Justice Ruth Bader Ginsburg died at 87 and Justice Amy Coney Barrett was confirmed to the high court, giving conservatives a 6-3 majority on the panel.
Vance's office is reported to be investigating hush money payments, made in the run-up to the 2016 election, to two women who both have alleged having sexual encounters with Trump. The president has denied the affairs.
In September, Vance's office revealed more information about his closely guarded inquiry, for the first time saying in a court filing that Trump could face a potential criminal tax probe.
Trump's efforts to conceal his financial information are unprecedented for a president in recent times. Since Richard Nixon, every president except for Gerald Ford and Trump have made their tax returns public.
In the first round of litigation, Trump's attorneys argued that presidents were entitled to temporary absolute immunity from state criminal investigations.
In a notable court exchange, one of Trump's attorneys argued that even if Trump shot someone on Fifth Avenue in New York, he could not be investigated until he left office.
The Supreme Court rejected that argument in July, with all nine justices — including those who otherwise sided with Trump — agreeing that presidents are not entitled to such sweeping immunity.
In a separate case decided on the same day, the court also said that the House of Representatives could obtain a subpoena for Trump's tax records, but struck down a lower court ruling in the Democratic-controlled chambers' favor, saying the House must meet a higher level of scrutiny.
After the Supreme Court rulings, Trump once again asked lower courts to allow him to keep his financial records private. Though he acknowledged he did not have absolute immunity, Trump argued that Vance's subpoena was still too broad and that it was issued in bad faith, amounting to "harassment of the President."
But those arguments didn't go anywhere. A federal district court rejected Trump's reasoning. In the opinion, District Judge Victor Marrero called it "absolute immunity through a back door." A three-judge panel of the 2nd U.S. Circuit Court of Appeals upheld the decision.
The congressional case has not returned to the Supreme Court yet, and is still being reviewed by an appeals court in Washington. A new Congress will take office in January, which could effectively end the matter.
Peter Shane, a professor at Ohio State University's Moritz College of Law, said it was not unusual that the court had not acted on the president's petition. It takes four justices to agree to hear a case, and they generally do so to resolve particularly high-profile matters or important unresolved questions of law.
"Although obviously a case in which a soon-to-be former president is involved is a noteworthy event, it's not clear that the legal issues are that noteworthy," Shane said. "They may intentionally be waiting until he's out of office. I don't know. It's not because the issues are weighty."
Shane said that he was speculating, as no one except for the justices and their staff knows what's really going on. But he added that he "could imagine the chief justice thinking that keeping things low profile for a while would be a contribution to the public impression of the court."
Chief Justice John Roberts, a George W. Bush appointee, is known to fiercely guard the court's reputation against criticism that it is partisan.
Possibly adding to Roberts' concerns, the top court has faced an unusual amount of scrutiny in recent weeks because of Trump's efforts there to overturn the results of the election.
On Tuesday, the justices turned back a lawsuit championed by conservatives that sought to overturn Biden's win in Pennsylvania. The justices dispatched with the case in a one-line order, with no noted dissents.
Also Tuesday, the state of Texas sued Pennsylvania and three other battleground states in a case it brought directly to the Supreme Court. Texas is seeking to erase Biden's wins in Pennsylvania, Georgia, Wisconsin and Michigan.
Trump quickly downplayed Tuesday's loss and trumpeted the Texas suit, though legal experts say it is not a serious case. The president has previously complained of the difficulty of getting the Supreme Court to review election cases, acknowledging that the justices likely would not take any.
On Wednesday, though, Trump said the Texas case is the one "everyone has been waiting for."
"It is very strong, ALL CRITERIA MET," the president tweeted.
Shane said that the election cases have similarities to the case over Trump's taxes.
"Although they involve a current and soon-to-be former president, the cases that are being presented to the court regarding the election — I'm trying to say this with a straight face — they don't present close questions of law," he said.
An attorney for Trump did not return a request for comment. Danny Frost, a spokesperson for the Manhattan district attorney's office, declined to comment.
Subscribe to CNBC Pro for the TV livestream, deep insights and analysis on how to invest during the next presidential term.